Re: Why Regularity?


Rupert wrote:
zuhair wrote:
Rupert wrote:
zuhair wrote:
Rupert wrote:
The reason why we have the axiom of regularity isn't really anything to
do with the liar paradox. It's just an indication of the fact that we
only want to study well-founded sets. In ZF-regularity we can prove
that the class of well-founded sets is a model for ZF with regularity
anyway.

I am speaking in a more philosophical manner, I see ZF as a theory of
finding consistency of statements of the that who always lies. All sets
in ZFC are lies. Yet , I said such M that all of its statements are
lies do have consistency, it is the consistency of the total lier,
though I call the later ( the opposite truth teller ) anyhow. This is
philosophical. Putting the axioms of regularity confines us to the lies
that are fairly consistent, it makes us avoid the lier paradox, which
reveal the philosophical truth to ZF. ZFC with Regularity is consistent
logically, but philosophically speaking, it is a system of consistent
lies, see the ulternative that I have proposed, I think this is the
HONEST set theory . But It seems not so practical. The Lieying ZF ( the
standard one ) is easier to deal with. And since all what we require
from a set theory is consistency, then it doesn't really matter if ZF
is philosophically a consistent lie. Since it easier to deal with, then
let it.

Zuhair

There is a mathematical analysis of the liar paradox. Tarski proved
that no language can define its own truth predicate. That's how the
liar paradox is avoided in mathematics.

As I say, I don't see what the liar paradox has to do with the axiom of
regularity.

You are not discriminating between , philosophy and mathematics.

Yes I am.

Read
what I wrote in another sense. in a philosophical sense. It is not
about regularity only, it is about the whole of ZFC, the theorym of
consistent lies.

Zuhair

I don't think you're doing philosophy, I think you're doing meaningless
gibberish.

I don't know why you like using these meaningless words. If you read
something you have to think about it, not just refuse it
straightforwards.

There is great similarity between Russells sets and the Lier paradox,
you should be blind not to see this.

Regularity aims at avoiding this paradox. If we use unrestricted
comprehension on ZF, and remove Regularity, then you will see ZF going
to its true nature. Just putting a restriction like regularity, though
avoids this paradox, but doens't let you reveal the truth of this
theory.
IF you are driving your car in the wrong direction, and you discovered
that, and reduced your spead so that you will not reach the wrong aim,
it doesn't mean that you are not driving in the wrong direction.
Regularity is only aviodance of what ZFC is heading at, i.e. Russells
set.
Regularity is like putting your hands in front of your eyes as not to
see the doom your are heading into, it doesn't change anything.

The direction should be changed.

If you remove regularity and make some directional modefication on the
theory like axiom2),3)4) I have wrote, and the axiom of infinity that I
need help with, you will find a theory that is as consistent as ZFC and
do not have problems with having a universe.

Any set theory which has a paradoxial universe, is a set thoery of
LIES. But it doesn't mean that it is not consistent, a theory that
always lies is a consistent theory,as far as it avoids its universe,
like ZFC, having Regularity as its braking power of avoidance of its
universe.

Zuhair

.

Relevant Pages

  • Re: Why Regularity?
    ... do with the liar paradox. ... Putting the axioms of regularity confines us to the lies ... ZFC with Regularity is consistent ...
    (sci.math)
  • Re: Why Regularity?
    ... do with the liar paradox. ... finding consistency of statements of the that who always lies. ... Putting the axioms of regularity confines us to the lies ... ZFC with Regularity is consistent ...
    (sci.math)
  • Re: Why Regularity?
    ... do with the liar paradox. ... finding consistency of statements of the that who always lies. ... Putting the axioms of regularity confines us to the lies ... ZFC with Regularity is consistent ...
    (sci.math)
  • Re: Why Regularity?
    ... do with the liar paradox. ... Putting the axioms of regularity confines us to the lies ... ZFC with Regularity is consistent ...
    (sci.math)
  • Re: Why Regularity?
    ... do with the liar paradox. ... Putting the axioms of regularity confines us to the lies ... ZFC with Regularity is consistent ...
    (sci.math)